Neutrino-mass determination from tritium $\beta$ decay: Corrections to and prospects of experimental verification of the final-state spectrum

We have investigated the final-state spectrum of ${\mathrm{HeT}}^{+}$ and ${\mathrm{HeH}}^{+}$ following $\beta$ decay of ${\mathrm{T}}_2$ or TH. For the electronically bound-state part of the spectrum the effects of a corrected recoil, improved potential curves for the excited states, nonadiabatic effects, and excitations of the initial molecular state have been investigated. We also discuss the feasibility of various experimental methods to verify the theoretical final-state spectrum.